8:57 AM PT -- TMZ Sports just spoke with Michael Lombardi ... and he called all of the rumors surrounding Bill Belichick nothing more than "fake news."

UNC general manager Michael Lombardi broke out his wet blanket Thursday and threw it all over rumors that Bill Belichick could leave Chapel Hill for the NFL ... insisting the coach is staying put.

Speculation that The Hoodie might bolt reached a boiling point on Thursday AM -- after it was revealed Belichick does NOT yet have a binding contract with the Tar Heels.

Bill only has a signed term sheet proposal -- according to CBS Sports' Jonathan Jones -- and it's caused many to wonder if that means he now could leave for an open NFL head coaching gig without consequence.

Lombardi, though, took to his X page and swore it was all irrelevant ... claiming Bill's not going anywhere.

"Bill is recruiting in DC today and Baltimore tomorrow," the Tar Heel GM said. "His focus is on North Carolina football, hiring staff members and developing the team. The NFL isn't a option so please stop making it one. Thank you."

He later added, "The reception towards UNC and Coach Belichick has been amazing from every school we visit. We are going to fight to keep North Carolina players here and bring the best to Chapel Hill."

Back in December -- when Bill first agreed to coach UNC's football team -- it didn't look like there'd be a spot for Belichick in the NFL's coaching carousel. However, since that time, several jobs have opened up -- including the sideline manager position in Dallas.

It's all sparked theories that Bill could pull up his stakes in North Carolina and go back to the pros ... but, again, Lombardi appeared to swear it won't happen.

Things could obviously change in the near future -- particularly if a fully executed and signed contract doesn't come to fruition.

Although, for now, stand down, Cowboys fans.